238
JACC Vol. 5, No.2
lACC
February 1985:238--48
A Format for Integrating the Interpretation of Exercise Ejection
Fraction and Wall Motion and Its Application in Identifying
Equivocal Responses
ALAN ROZANSKI,
ROZANSKI. MD, * GEORGE A. DIAMOND, MD, FACC, * ROBERT JONES, MD, FACC,:!:
JAMES S. FORRESTER, MD, FACC,* DANIEL BERMAN, MD, FACC,* DENISE MORRIS, BS,*
BRAD H. POLLOCK, MPH,* MICHAEL FREEMAN, MD,t H. J. C. SWAN, MD, PHD, FACC*
Angeles. California,
California. Toronto, Ontario, Canada and Durham, North Carolina
Los Angeles,
The conventional interpretation of ejection fraction change
with exercise may be limited because it does not consider
the rest value, define equivocal responses or integrate
wall motion data reproducibly. Thus, a format was developed for combined interpretation of rest and exercise
radionuelide ejection fraction and wall motion by reviewing the reported data for the exercise responses of
patients without prior myocardial infarction. The ejection fraction data of 202 normal patients and of 259
patients with coronary artery disease were first fitted to
beta distributions. The true positive and false positive
rates for coronary disease for each combination of rest
and exercise ejection fraction were then determined directly from these distributions. A given rest/exercise
ejection fraction combination was "normal" if the false
positive rate was greater than the true positive rate, or
"abnormal" if the true positive rate was greater than
the false positive rate, and "equivocal" when the rates
were similar (within a 50% confidence interval).
Although exercise radionuclide ventriculography is now well
established as a diagnostic test for coronary artery disease,
the criteria for its interpretation vary considerably. For example, no fewer than five mutually incompatible and arbitrary thresholds are currently employed for categorizing
the exercise ejection fraction response: an absolute increase
of 0 (I), 5 (2), 6 (3) and 7% (4), and a relative increase of
From * the Division of Cardiology and Department of Nuclear Medicine, Cedars-Sinai Medical Center, and the Department of Medicine,
UCLA School of Medicine, Los Angeles, California; t the Department of
Medicine, SI. Michael's Hospital, Toronto, Ontario, Canada; and t the
Medicine.
Departments of Surgery and Radiology, Duke University Medical Center,
Durham, North Carolina. This study was funded in part by SCOR Grants
17651 and 17670 from the National Institutes of Health, Bethesda, Maryland and a Grant-in-Aid to Dr. Rozanski from the American Heart Association, Greater Los Angeles Affiliate, Inc., Los Angeles, California.
Manuscript received June 28, 1983; revised manuscript received July 17,
1984, accepted September 6, 1984.
Address for reprints: Alan Rozanski, MD, Division of Cardiology,
Cedars-Sinai Medical Center, Los Angeles, California 90048.
Clj 1985 by the American College of Cardiology
This analytic format, which predicted an inverse relation between rest ejection fraction and the change required with exercise, was then validated prospectively
in 854 patients without myocardial infarction (557 with
and 297 without angiographic coronary artery disease).
Using the conventional criterion of an abnormal test
result «0.05 absolute rise in ejection fraCtion with exercise or a wall motion abnormality), sensitivity was 85
± 2% and specificity only 42 ± 3%. The statistical
format had a ~ensitivity of 70 ± 2 % and specificity of
inform~tion
70 ± 3%, resulting in a twofold increase in inform~tion
content. This .format has at least two advantages over
conventional interpretation: 1) it provides an explicit
definition of equivocal responses; and 2) it reproducibly
integrates discordant ejection fraction and wall motion
responses and allows for the combined analysis of other
nonscintigraphic observations, such as age and sex.
(J Am Coli CardioI1985;5:238-48)
10% (5). It follows that some responses interpreted as "normal" at one institution would be interpreted as "abnormal"
at another. Moreover,. interpretation of the wall motion response is often discordant with that of ejection fraction, and
no explicit method of unifying such conflicting observations
has been proposed. As a result, the final interpretation is
often highly subjective and not reproducible. The purpose
of this study, therefore, was to develop an algorithm that
allows the integrated interpretation of wall motion and ejection fraction, and to compare the accuracy of this algorithm
with that of conventional analysis.
Methods
Data Base
The study group consisted of I ,316 patients undergoing
first pass or gated equilibrium radionuclide ventriculography
at rest and during exercise.
0735-1097/85/$3.30
239
ROZANSKI ET AL.
W ALL MOTION
EJECTION FRACTION AND WALL
lACC Vol. 5. No.2
February 1985:238-48
Retrospective patients (used for algorithm development). Previous studies published in the English language
from 1977
1977 to 1983
1983 were reviewed to select a group of
patients without prior myocardial infarction who underwent
both rest and exercise radionuclide ventriculography and
coronary angiography. The minimal selection criteria were
(N).
that the published report include the number of patients (N),
the mean ejection fraction and the standard deviation (SO)
or standard error of the mean (SEM) both for rest and peak
reported.
exercise. If only the standard error of the mean was reported,
it was converted to standard deviation according to the formula: SO = SEMVN. Studies containing healthy volunteers or patients with prior myocardial infarction were totally
excluded from analysis unless such patients could be identified and excluded on an individual basis.
(4,6--25) describing 462
(132
462 patients (132
Twenty-one reports (4,6-25)
with first pass and 330
330 with equilibrium studies) were idenI). Angiographically
tified and analyzed separately (Table 1).
259
"significant" coronary artery disease was present in 259
(56%) and absent in 203
203 (44%).
(44%). Since there were no sys(56%)
tematic differences in the ejection fraction response between
(26-32), the data
the first pass and equilibrium techniques (26-32),
214 patients, individual rest and exercise
were pooled. In 214
(117 with and 97
ejection fraction values were tabulated (117
97
without coronary artery disease). These data were used to
estimate the correlation (r
(r22 = 0.32)
0.32) and covariance (I:T
(O"xy
xy =
0.009)
between
rest
and
exercise
ejection
fraction.
0.009)
Prospective patients (used for algorithm valida274 patients studied by the
tion). This group comprised 274
equilibrium technique at Cedars-Sinai Medical Center or St.
580 patients studied by the first pass
Michael's Hospital and 580
technique at Ouke University Medical Center. Each of these
854
3 months
854 patients underwent coronary angiography within 3
of rest and exercise radionuclide ventriculography as part
of the clinical evaluation for suspected coronary artery disease. None had a previous or intervening myocardial infarction. valvular heart disease, congenital heart disease or
farction,
nonischemic cardiomyopathy. The mean age (± SO) was
53
53 ± 9
9 years and 67%
67% were male. There were 557
557 patients
(2::50% diameter stenosis of
with coronary artery disease (2::50%
287 (34%)
(34%) had triple
any major coronary artery), of whom 287
(15%) had double vessel disease and
132 (15%)
vessel disease, 132
138
(\ 6%) had single vessel disease. The remaining 297
297
138 (16%)
patients (35%)
(35%) had normal coronary arteriograms or angio«50% diameter narrowing).
graphically insignificant disease «50%
Exercise scintigraphy in prospective patients. Upright
200 kpm/min and increased
bicycle ergometry was begun at 200
in stages until a maximal effort was achieved, unless ex-
Table 1. Literature Review of Rest and Exercise Ejection Fraction
Patients With Normal Coronary Arteriogram
Reference
No.
Rest EF ( ± SO)
Patients With Coronary Artery Disease
EX EF (±SO)
No.
Rest EF ( ± SO)
EX EF (±SO)
20
II
\1
0.65 ± 0.07
0.10
0.53 ± 0.\0
0.64 ± 0.11
0.39 ± 0.09
48
0.63 ± 0.10
0.61 ± 0.12
II
1\
0.64 ± 0.06
0.58 ± 0.10
0.66
0.64
0.58
0.66
0.64
0.67
0.63
0.65
0.58
0.54
0.46
0.60
0.66
0.59
Equilibrium (gated pool) Studies
4
6
7
8
9
10
21
2\
29
II
11
15
6
24
II
12
13
14
\4
15
16
17
18
II
21
138
Total
0.61
0.63
0.60
0.59
0.70
0.63
±
±
±
±
±
±
0.09
0.12
0.05
0.05
0.09
0.09
0.65 ± 0.06
0.65 ± 0.07
0.63 ± 0.09
0.70
0.70
0.63
0.70
0.80
0.73
±
±
±
±
±
±
0.09
0.14
0.09
0.07
0.11
0.09
0.75 ± 0.08
0.73 ± 0.08
0.71 ± 0.\0
0.10
lUI
10
20
28
7
18
19
\9
192
±
±
±
±
±
±
±
0.07
0.06
0.09
0.05
0.17
0.08
O.OS
0.08
±
±
±
±
±
±
±
0.09
0.10
0.12
0.13
0.10
0.12
0.11
First Pass Studies
19
20
21
22
23
24
25
Total
IS
15
0.66 ± 0.04
O.OS
0.79 ± 0.08
3
10
10
16
9
12
65
0.70
0.71
0.61
0.6\
0.67
0.62
0.65
0.07
0.11
0.12
0.15
0.06
0.10
0.76 ± 0.09
0.79 ± 0.09
0.80±0.12
O.80±0.12
OS4 ± 0.15
084
0.75 ± 0.04
0.79 ± 0.10
Pooled total
203
0.64 ± 0.09
0.74 ± 0.10
EF
=
±
±
±
±
±
±
fraction, denoted in the text as
ejection fraction.
25
9
0.70 ± 0.07
0.71 ± 0.11
0.64 ± 0.13
0.62 ± 0.07
21
2\
0.53 ± 0.15
0.45 ± 0.12
12
67
0.10
0.55 ± 0.\0
0.62 ± 0.11
0.49 ± 0.12
0.55 ± 0.12
259
0.63 ± 0.09
0.11
0.58 ± 0.\1
p; EX == exercise; SO = standard deviation,
denoted in the text as
0".
240
No.2
lAce Vol. 5, NO.2
February 1985:238-48
ROZANSKI ET AL.
EJECTION FRACTION AND WALL MOTION
ertional hypotension, serious ventricular arrhythmias or
marked chest pain supervened. All studies were performed
under constant electrocardiographic monitoring, using a
V5s lead to assess cardiac rhythm and heart rate.
modified V
Blood pressure was measured indirectly with a sphygmomanometer. The first pass imaging technique employed an
anterior projection, a multicrystal gamma camera (Baird
System Seventy-Seven) and IO to 15 mCi of technetium99m pertechnetate injected both at rest and peak exercise.
The equilibrium technique employed 45° left anterior oblique
projection, a single 0.25 inch sodium iodide crystal, an all
purpose collimator and 25 mCi of technetium-99m in
vitro labeled autologous red blood cells injected before exercise. The details of each method have been reported previously (3,33).
Count changes within a left ventricular region of interest
were used to identify end-diastolic and end-systolic frames.
Ejection fraction was then calculated by dividing stroke
counts (end-diastolic minus end-systolic) by the background-corrected end-diastolic counts. All ejection fraction
data in this study are expressed as absolute decimal values.
Interpretation of wall motion and ejection fraction. Each left ventricular segment (anterior, apical and
inferior for the anterior view; septal, inferoapical and posterolateral for the oblique view) was assessed in a closed
loop video display by two or more experienced observers
who were unaware of the clinical data. Wall motion was
interpreted subjectively and then reduced to a four point
ordinal scale: 0 == normal, I = mild to moderate hypokinesia, 2 = moderate to marked hypokinesia and 3 ==
akinesia or dyskinesia. Any score less than 0 in any myocardial segment was considered "abnormal." A "normal"
ejection fraction response to exercise was defined using the
most common conventional criterion, that is, an absolute
increase of 0.05 or more during exercise (2).
Algorithm development. The 462 patients obtained from
published reports (retrospective group) were used to develop
a statistical format for interpretation of ejection fraction and
wall motion (see Appendix I). This format was then applied
to the interpretation of individual responses in the 854 institutional patients (prospective group).
Ejection fraction. Briefly, the mean (p) and standard
deviation (a) of pooled ejection fraction data for each of
the four groups in Table I (rest and exercise.
exercise, with and
without disease) were converted to beta probability distributions (34,35), from which the true and false positive rates
relative to angiographic coronary artery disease were determined for each of 60 levels of rest ejection fraction (rangO.OI), and for each
ing from 0.20 to 0.80 in increments of 0.01),
0£40 levels of exercise ejection fraction (ranging from + 0.20
to - 0.20 relative to the rest value, also in increments of
O.OI). The true and false positive rates for each of the 40
0.01).
x 60 or 2,400 rest/exercise combinations were calculated
multiplicatively, and a 50% confidence interval was employed to compare the magnitude of difference between
these rates: when the true positive rate was greater than the
false positive rate (with 50% confidence), the associated
restiexercise ejection fraction combination was considered
rest/exercise
"abnormal"; similarly, when the false positive rate was
greater than the true positive rate, the combination was
considered "normal"; if, with 50% confidence, the two
were not different, the combination was considered "equivocal. " To incorporate consideration of age and sex into this
model, we stratified the men and women separately by deciles of age, determined the age- and sex-specific beta distributions for each subgroup, and reanalyzed each of the
854 ejection fraction responses using the resultant distributions (Fig. I).
Wall motion. To extend this analytic format to additional consideration of wall motion, one needs to know the
frequency distribution of ejection fraction in the normal and
abnormal wall motion subsets of the pooled groups of patients summarized in Table I. Since these data could not
be obtained from our literature review, we estimated the
needed values from our institutional data by assuming differences in wall motion to be the proximate cause of differences in ejection fraction. Accordingly, the frequency
of abnormal wall motion is given by the equation:
0.04 r - - - - - - - - - - - - - - - - - ,
Figure 1. The statistical analysis of ejection fraction.
This figure illustrates the beta frequency distribution
of exercise ejection fraction (EF) in the angiographinormal patients (NCA) (EF = 0.74 ± 0.10) and
cally nonnal
the patients with coronary artery disease (CAD) (EF
= 0.58 ± 0.11). The true positive and false positive
rates for any subsequently observed ejection fraction
determined directly
value (0.55, for example) were detennined
from the curves. The reason each rate is so low is that
it represents the frequency only for that particular value.
Rest ejection fraction was analyzed similarly.
~
0.03
.
CAD
~i.~y.~.Rg~...':.~.·.Q.!~...............
':.~.·.Q.!~............... ..
..:r.~I.!~ .. ~i.~y.~.Rg~
NCA
Z
~ 0.02
lJ.I
IJJ
0::
u.. 0.01
o
0.55
EJECTION FRACTION
1.0
ROZANSKI ET AL.
WALL MOTION
EJECTION FRACTION AND WALL
lACC Vol. 5. No.2
February 1985:238-48
F = (L - N)/(A - N), where F is the estimated frequency
of abnormal wall motion in the pooled patients from the
published reports, L is the average ejection fraction in that
group, N is the average ejection fraction in the subset of
institutional patients with normal wall motion and A is the
average ejection fraction in the subset of institutional patients with abnormal wall motion. Ifwe make the reasonable
assumption that F is beta-distributed, we can then estimate
the frequency of mild, moderate and severe wall motion
abnormality by fractional integration of this function. These
data are incorporated into the FORTRAN computer program
listed in Appendix II. Using this program, we analyzed each
combination of resUexercise wall motion and ejection fraction for each of the 854 institutional patients in a manner
identical to that already described for ejection fraction alone.
Statistical analysis. Ejection fraction mean values were
compared using the unpaired t test. Standard deviations for
sensitivity and specificity were expressed as standard error
of the percent, y'P(I - P)/N, where P is the proportion,
N the size of the group from which the proportion was
estimated and I the average information content.
The accuracy of a given sensitivity/specificity combination was defined by its average information content (I) (36):
1I = (TPxP)log
(TPXP)!Og2(TPxP)
(FPXQ)]Og2(FPxQ)
2 (FPxQ)
2(TPxP) + (FPxQ)log
- (TPxP + FPxQ)log
FPXQ)!Og22 (TPxP + FPxQ)
- Plog 22P + (FNxP)log 22 (FNxP) + (TNxQ)lOg2(TNxQl
(TNxQ)lOg2(TNxQ)
QIOg2Q.
- (FNxP + TNxQ)log 2 (FNxP + TNxQ) - Qlog
2Q.
where TP = true positive rate or sensitivity, FN = false
negative rate (I - TP), FP = false positive rate or 1specificity, TN = true negative rate (I - FP), P = prevalence
aence and Q =: I - P, each as a decimal.
Information content is usually expressed in binary digits
(bits) when only two outcomes are under consideration (disease and nondisease). Because this unit is unfamiliar to
most, we converted it to a ratio relative to conventional
+30
+20
+10
lL.
w
W
<l
00
....
.....
·::i·
.11 •
·v.·
...•·
...
.... ........•••...:...
analysis. Thus, an information content of 0.5 represents half
the accuracy of conventional analysis, while an information
content of 2 represents twice the accuracy.
Results
Ejection fraction response to exercise. Figure 2 illustrates the change in left ventricular ejection fraction (AEF)
for each of the 854 prospective patients. The response of
the normal patients and patients with coronary artery disease
overlapped widely. Using the conventional criterion of abnormality (AEF < 0.05), an abnormal exercise ejection
fraction response was present in 430 of the 557 patients
with coronary artery disease (sensitivity = 77 ± 2%), but
ISO of the 297
a normal response was observed in only 150
patients without disease (specificity = 51 ± 3%). Information content averaged 0.04 bits, only 6% of that provided
by coronary angiography. This value served as the standard
with which all other interpretive criteria were compared.
The statistical relation between rest and exercise ejection
fraction (developed from 462 patients from the published
data, using a 50% confidence interval to define "normal,"
"equivocal" and "abnormal" responses) is illustrated in
Figure 3. This format demonstrated an inverse relation between the rest ejection fraction and the absolute amount by
which ejection fraction must increase with exercise for the
combination to be judged normal. For example, if rest ejection fraction is 0.55, it must increase by 0.13 to 0.68 for
the exercise response to be normal, but it need not increase
at all if the rest ejection fraction is 0.65, and may even
decrease by 0.09 to 0.66 if rest ejection fraction is 0.75.
For each rest ejection fraction value, a small range (about
0.04 in width) encompassed the equivocal zone. Within this
zone, the combination of rest and exercise values was statistically no more likely to be observed in the presence of
disease than in the absence of disease.
..:
.~:I:
····:i_'i.
. . Ill··Y•••••
:!
•
••••••
Jl.tl.
Figure 2. Change in left ventricular ejection fraction
from rest to exercise (AEF) for each of the 297 subjects with normal coronary arteriograms (NCA) (left)
and each of the 557 patients with coronary artery
disease (CAD) (right).
.:-~
• I I
-10
-20
241
i
..I
1.;'11.\:
:-::
-:=-
-30
...=.
NCA PATIENTS
CAD PATIENTS
242
ROZANSKI
AL.
ROZANSKI ET
ET AL.
WALL MOTION
EJECTION
AND WALL
EJECTION FRACTION
FRACTION AND
MOTION
No. 2
lACC Vol. 5.
5, No.2
February 1985:238-48
sification . The 123 patients (72 with coronary disease, 51
sification.
without) classified conventionally as abnormal but statistically as normal were characterized by a high rest ejection
fraction, averaging 0.73 ± 0.08. Conversely, in the 35
patients (25 with coronary disease, 10 without) reclassified
as abnormal by our format, the rest ejection fraction was
0.46 ± 0.09 (p < 0.03 compared with the former). The
rest ejection fraction was intermediate in the 139 patients
whose responses were reclassified as equivocal (0.65 ±
0. 10).
0.10).
age . Although rest ejection fraction valRole of sex and age.
ues did not vary with age and sex, peak exercise values
tended to be lower with advancing age and in women (Table
2) . When these stratified ejection fraction data were incor2).
porated into our model, sensitivity increased to 69 ± 2%
(271 of 391), specificity increased to 73 ± 3% (140 of 193)
2.1 . However, the
and information content increased to 2.1.
percent of patients whose responses were equivocal also
doubled from 16 to 32%.
fraction . Rest and exercise
Rest versus exercise ejection fraction.
ejection fraction were also analyzed separately, again using
a 50% confidence interval to define normal, equivocal and
abnormal values. According to this analysis, rest values of
0 .61 and exercise values of 0.61
0 .61 to 0.62 were equiv0.58 to 0.61
ocal . The best discrimination between patients with and
ocal.
without coronary artery disease was provided by the combined rest/exercise format. Exercise ejection fraction alone,
3) .
however, was almost as good (Table 3).
wan motion. Combined conAdditional assessment of waU
ventional analysis of wall motion and ejection fraction provided little improvement in diagnostic discrimination. Either
the wall motion or ejection fraction response was abnormal
in 472 of the 557 patients with coronary artery disease
al so in 171 of the 297 patients
(sensitivity = 85 ± 2%), but also
:t 3%). Information conwithout disease (specificity = 42 :t
tent was 1.
1.11 relative to conventional analysis.
of ejection fraction and
The combined statistical analysis of
5 . Concordant ejection
wall motion is illustrated in Figure 5.
fraction and wall motion responses,
responses , when normal,
normal , were
normality , and
associated with a larger confidence zone for normality,
when abnormal, a larger confidence zone for abnormality.
+20
+10
0~
~
u..
u.
w
w
0
<l
-10
-20
_ _L...-_
__
_
40
60
20
RESTING EF (%)
~
~
~
L...-_~
L
...-_~
80
Figure 3. Diagnostic interpretation of 2,400 rest/exercise ejection
fraction combinations, based on a 50% confidence interval. The
x axis is rest ejection fraction. The y axis displays change in
(AEF) , rather
ejection fraction (AEF),
rather than exercise ejection fraction, to
allow a direct comparison with the conventional criterion. (The
conventional criterion considers all values of AEF < 0.05 as abnormal , regardless of the rest value, and does not define an equivnormal,
figures , the
ocal range.) For each graph in this and all subsequent figures,
" abnormal" redark gray zone defines the statistical region of "abnormal"
" equivocal" responses
sponses , the light gray zone defines the "equivocal"
sponses,
"normal " responses (see text).
and the white zone defines the "normal"
of the 854 prospective patients by our statistical
Analysis ofthe
format is illustrated in Figure 4 .. 139 responses (16%) were
classified as equivocal, 92 (17%) in the 557 patients with
coronary disease and 47 (16%) in the 297 patients without
NS) . In those whose responses were not clasdisease (p = NS).
equivocal , sensitivity was 66 ± 2% (309 of 465)
sified as equivocal,
comparison ,
and specificity was 64 ± 3% (161 of 250). For comparison,
we excluded a similar number of patients from consideration
using the conventional criterion by arbitrarily defining a ~EF
0 .03 to + 0.07 as equivocal. As a result, sensitivity
from + 0.03
was 83 ± 2% (394 of 473) and specificity was 49 ± 3%
245) . Both of these differences were significant
(120 of 245).
compared with our statistical format
format,, although information
content increased only to 1.2.
J58 patients (19%)
( J9%) were reclassified into the
A total of 158
f ormat. For these paopposite category by the statistical format.
tients, the rest ejection fraction-and not its change with
exercise-was the primary determinant causing this reclas-
+
20 .-------.-,...........--.........--...,
+20
~--~~~=r--~
CAD
+10
Figure 4. Individual rest and exercise ejection fraction (AEF) responses for the 557 patients with coronary artery disease (CAD) and the 297 patients with
normal coronary arteriograms (NCA). Patients with
coronary artery disease tended to have more abnormal
responses; patients with normal coronary arteriograms tended to have more normal responses
responses.. However, in each case, the degree of overlap is substantial.
u..
u.
w
•
o
• •
••
.•
•
•
•
•
<l
-10
-20
-20
•
NCA
•
•
.. : .. .
•••
••
_
...--LII_
__
_LL...--&011_
40
20
40
60
80 20
RESTIN
G EF (%)
RESTING
I
....
"."
••••••
~
20
60
80
243
ROZANSKI ET AL.
EJECTION FRACTION AND WALL MOTION
JACC Vol. 5.
5, No.2
February 1985:238~48
Table 2. Peak Ejection Fraction Values According to Age and Sex
<35
36 to 45
46 to 55
56 to 65
>65
70
68
68
65
58
±
±
±
±
±
9 (22)
II (68)
(\ 16)
12 (\16)
(75)
13 (75)
(16)
12 (\6)
60
59
58
57
53
±
±
±
±
±
13
13
14
13
12
(II)
(78)
(214)
(200)
(54)
CAD
NCA
CAD
NCA
Female
Male
All Patients
Age
Decile
7J
70
71
66
61
±
± 7(13)
7(\3)
± II (39)
±
10 (48)
± 10
±
(32)
± 13 (32)
IX (7)
± 18
63
59
57
57
51
±
± 9 (7)
± 9 (65)
±
14 (178)
±
± 14(178)
± 14 (142)
IO (39)
± 10
CAD
NCA
63
60
65
65
55
(9)
± 10 (9)
±
±
±
±
±
±
±
±
II (29)
13 (68)
13 (43)
7 (9)
50
57
6\
61
59
57
±
±
±
±
±
±
±
±
22
14
15
12
± 16
(4)
(4)
(13)
(\3)
(36)
(58)
(15)
(\5)
disease; NCA = normal coronary arteriograms or angiographically
Numbers in parentheses represent the number of patients. CAD = coronary artery disease:
insignificant disease «50% diameter narrowing).
The concomitant statistical assessment of ejection fraction
and wall motion, therefore, reduced the number of equivocal
interpretations by 74% from 139 to 36, and 71 of these 103
reclassifications were correct relative to angiography. Additional analysis of segmental wall motion also resulted in
88 new patients being reclassified as having an equivocal
response. In 59 of these, the ejection fraction and wall
response,
motion responses were discordant (one normal and the other
analysis, Excluding all 124 (36
abnormal) by conventional analysis.
+ 88) equivocal classifications, the combined analysis of
ejection fraction and wall motion resulted in a sensitivity
of 70 :±: 2% and a specificity of 70 :±: 3%, representing a
2.2 increase in information content relative to conventional
analysis. In general, incorporation of wall motion into our
analysis,
model tended to improve accuracy by increasing sensitivity
in the patients with imaging by the gated equilibrium technique, and by increasing specificity in the patients with
imaging by the first pass technique (Table 4).
Discussion
Advantages of statistical algorithm. The conventional
criterion for diagnosis of coronary artery disease by radionuclide ventriculography has two important limitations. First,
restriction of analysis to the magnitude of ejection fraction
change alone needlessly discards a substantial amount of
potentially important information. For example, since a change
in ejection fraction (6EF) is governed largely by the level
of the rest ejection fraction (37-39), consideration of the
latter might improve diagnostic accuracy. Second, the two
scintigraphic variables most often analyzed, namely, global
ejection fraction and regional wall motion, are often discordant (30% of the time in our data), and there is no
generally accepted method for reconciling their differences.
It was to overcome these limitations that we designed a
statistical algorithm based on the pooled experience of 21
investigative groups. This algorithm predicted an inverse
relation between rest ejection fraction and 6EF. That is, the
higher the rest ejection fraction, the less it had to increase
during exercise to be interpreted as "normal." In fact, if
the rest ejection fraction was more than 0.65 and exercise
wall motion was normal, even a decrease in ejection fraction
with exercise could be considered normal. Our algorithm,
therefore, differs in important ways from conventional analysis, whereby only the absolute level of AEF is considered.
Accuracy of the method. Neither approach, however,
yielded high sensitivity and specificity in this study. Rather,
our prospective analysis indicated a wide overlap of ejection
fraction responses between normal patients and patients with
coronary artery disease. This overlap was so great that it is
unrealistic to expect that any method of analysis could circumvent the low specificity inherent in the data. We could
not, for example, identify any categorical cutpoint that would
significantly improve diagnostic accuracy over that derived
from the 0.05
0,05 criterion. When we expanded our analysis to
include both the rest and exercise ejection fraction values,
the wide overlap between those with and without coronary
artery disease persisted. Thus, our format significantly improved specificity in comparison with conventional methods, but only at the expense of sensitivity. Only when we
integrated additional information into our model, such as
age and sex or the interpretation of wall motion, did information content improve.
Limitations of prospective validation. An important
limitation of our prospective validation was the distortion
popUlation introduced by two forms of referral
in the study population
Table 3. Comparison of Rest and Exercise Statistical Fonnats
Formats
Rest EF
Exercise EF
Rest/exercise EF
EF = ejection fraction.
Proportion of
Equivocal Responses
Sensiti vity
Specificity
Information
Content
127/854 15 ± 1%
100/854 12 ± 11%
%
139/854 16 ± 1%
170/486 35 ± 2%
309/504 61 ± 2%
309/465 66 ± 2%
1681241
\68124\ 70 ± 3%
1711250 68 ± 3%
161/250
\61/250 64 ± 3%
0.02
l.05
1.05
l.15
1.15
244
JACC Vol. 5.
5, No.2
February 1985:238~8
ROZANSKI ET AL.
EJECTION FRACTION AND WALL MOTION
WALL
REST
MOTION
NORMAL
NORMAL
UNDETERMI~
UNDETERMI~
ABNORMAL
NOR~L[SJ[SJ[§J
~ u«mMI~I\lI\l~
~L)jLjj
X
w
A8~ALI'\lI\l.~
~~~
Figure 5. Combined statistical analysis of rest/exercise ejection
fraction and wall motion. Nine wall motion combinations are illustrated; three for rest and three for exercise. The middle panel
is identical to Figure 3 and represents no knowledge of the wall
motion response (termed "undetermined"). Concordantly normal
rest and exercise wall motion resulted in the largest confidence
zone for normality (upper left) while the largest zone for abnormality was present when both wall motion and ejection fraction
were abnormal (lower right). For simplicity, the axes of each
graph are not labeled, but are identical to previous figures.
(40,4 I). The first is pretest referral bias, whereby the
bias (40,41).
selection of an unrepresentative group of patients can seriously affect the frequency and magnitude of normal test
responses (40). This bias can be minimized if atypically
healthy and sick groups are not included in analysis (for
example, healthy volunteers and postinfarction patients),
and we took the precaution of excluding such patients in
the development and application of our algorithm. Less
avoidable, however, is post-test referral bias, the preferential referral of positive test responders to angiography and
negative responders away from angiography (41). Such
practice, although clinically sound, serves to increase the
overlap of abnormal functional responses in our angiographic population, deflating specificity while increasing
sensitivity. It may be impossible to judge the true accuracy
of any test in such patients. In contrast, the improved accuracy of our format is best illustrated by applying it to
groups of patients not subject to this bias. For example,
Foster et al. (38) observed a 67% false positive rate in 42
volunteers during maximal exercise using the conventional
criterion, but we would classify only 3% of them as abnormal by our format. The reclassified normal subjects are
those with a high rest ejection fraction which did not increase
to the expected degree with exercise. Of note, other investigators (42-44) concluded that many patients with normal
coronary arteriograms do not increase their exercise ejection
fraction if they have a high rest value.
Limitations in pooling of data. Our format is based on
the pooled experience of many investigators. There are several problems with this approach. The first relates to differences in methodology. Different exercise protocols, imaging hardware and processing techniques all affect test
results. The first pass technique, for example, is geared more
toward high count rates, while the gated equilibrium technique is geared more toward high resolution. For determination of ejection fraction, these differences appear to be
of little consequence: rest and exercise ejection fraction
values are nearly the same in patients tested with both techniques (26-32), and our literature review revealed that avI).
erage ejection fraction values were very similar (Table 1).
Technical differences may be more significant for wall motion assessment, however. The single crystal detector used
with the gated equilibrium technique is inherently less sensitive (relative to count rate detection) and of higher resolution, while the multicrystal detector used with the first
pass technique is more specific since it is less likely to
resolve minor abnormalities,
abnormalities. It is not surprising, therefore,
that incorporation of wall motion into our format tended to
improve sensitivity in the patients imaged by the gated technique and specificity in the patients imaged by the first pass
technique. This trend suggests that stratification of our model
according to the technique employed may improve its overall accuracy.
Role of age and sex. The publications included in our
literature review did not stratify the ejection fraction responses by age and sex. We, therefore, had to rely on our
own data to incorporate these variables into our model. As
with the analysis of wall motion, these refinements improved
accuracy. Thus, our data support the view that age and sex
affect left ventricular function independent of coronary anatomy (3,45-48). Unlike the analysis of wall motion, however, stratification by age and sex increased rather than
decreased the number of equivocal responses, probably be-
Table 4. Comparative Accuracy
Ejection Fraction
Ejection Fraction and Wall Motion
Patients
Sensitivity
Specificity
Sensitivity
Specificity
All (n = 854)
First pass (n = 580)
Gated equilibrium (n = 274)
± 2%
66 ±
± 2%
2%
62
62 ±
77 ±
± 3%
64
64 ±
± 3%
63 ±
± 3%
± 5%
67 ±
70 ± 2%
63 ± 2%
86
86 ± 3%
3%
70 ± 3%
73 ± 3%
3%
73
64 ± 5%
64
245
ROZANSKI ET AL.
EJECTION FRACTION AND WALL MOTION
JACC Vol. 5. No.2
February 1985:238-48
cause this subdivision resulted in very small samples. InmUltiple variables, therefore, results in a
corporation of multiple
tradeoff between accuracy and precision.
Clinical relevance. The purpose of developing our format was to provide a logical and reproducible empiric method
for analysis of radionuclide ventriculographic test responses.
Since the conventional categorical method is also empiric,
we were not surprised that our format resulted in only a
modest improvement in overall accuracy of interpretation.
In our view, however, traditional emphasis on accuracy
alone tends to overlook other equally important criteria for
test evaluation. It is by these additional criteria that we
believe our format is to be preferred to conventional analysis.
Equivocal responses can be defined. Some test responses
are likely to occur with equal frequency in patient groups
with and without disease. Conventional analysis, however,
requires that every response be characterized categorically
as either "normal" or "abnormal." Our format, on the
other hand, allows those responses that occur with similar
frequency in both the presence and absence of disease to
D
16°/(,
be characterized as "equivocal." In this study, 16
ID of
ejection fraction responses were so characterized. Such classification does not imply inadequate information or poor
technique; rather, it recognizes that physiologic responses
fall along a continuum. The likelihood ratio of an equivocal
response (the true positive rate divided by the false positive
rate) averaged 1.1 ± 0.2 (p = NS versus unity), confirming
the appropriateness of this classification. By extending our
format, one can further characterize individual responses as
"strongly" normal or abnormal relative to other confidence
levels, (95%, for example) thereby allowing diagnostic certainty to be expressed as a continuous function.
Additional data can be integrated. Currently, the interpretation of a discordant ejection fraction and segmental
waII
wall motion response is highly subjective and poorly reproducible. In our data, the addition of wall motion assessment to the conventional analysis of ejection fraction
did not improve diagnostic accuracy; sensitivity increased
by 8%, but specificity decreased by 9%. In contrast, comwaII motion
bined statistical analysis of ejection fraction and wall
resulted in a 10% reduction in the number of equivocal test
responses, while sensitivity and specificity both increased
compared with the analysis of ejection fraction alone, and
information content improved twofold.
waII motion, other important clinical inIn addition to wall
formation can be readily incorporated into the analyses. For
example, Table 5 illustrates the integration of scintigraphic
and clinical data in a 60 year old woman who complained
of nonexertional substernal discomfort that was promptly
relieved by nitroglycerin. She had a systolic blood pressure
of 140 mm Hg and a normal electrocardiogram at rest. She
exercised for 9 minutes to a heart rate of 160 beats/min and
a systolic blood pressure of 190 mm Hg and developed 2
mm slow upsloping ST segment depression during recovery.
On the basis of Bayesian analysis of these data (49,50), her
probability of coronary artery disease was 54 ± 18%. Table
5 summarizes the interpretation of nine hypothetical ejection
waII motion responses by the conventional and
fraction and wall
statistical formats. In each case, the direction and magnitude
of change in the probability of coronary artery disease as a
consequence of testing (weighted for the achieved level of
stress [50]) corresponds with the statistical interpretation.
Probability decreases substantially when the interpretation
is normal, increases when the interpretation is abnormal and
changes little when the interpretation is equivocal. Although
a similar integration of clinical and scintigraphy data has
been accomplished by multivariate analysis from individual
laboratories (39,48,51), this method has not been widely
employed, probably because it is not necessarily prospectively applicable in a different laboratory.
Conclusion. Our statistical algorithm provides an alternate paradigm for diagnostic test interpretation based on the
pooled experience of many investigators. This format possesses distinct advantages compared with conventional analysis. It explicitly identifies equivocal test responders, integrates the interpretation of ejection fraction and wall motion,
Table 5. Bayesian Analysis of Radionuclide Data
Ejection Fraction
Regional Wall Motion
Interpretation
Post-Test
CAD
Probability
Change
in CAD
Probability
Rest
Exercise
Rest
Exercise
Conventional
Statistical
(ric)
(%)
(%)
0.68
0.50
0.45
0.45
0.75
0.65
0.65
0.70
0.75
0.75
0.43
0.45
0.53
0.68
0.70
0.70
0.70
0.75
Nonnal
Mild hypokinesia
Nonnal
Nonnal
Nonnal
Nonnal
Nonnal
Nonnal
Nonnal
Nonnal
Mild hypokinesia
Nonnal
Nonnal
Nonnal
Nonnal
Moderate hypokinesia
Nonnal
Mild hypokinesia
Nonnal
Abnonnal
Abnonnal
Nonnal*
Abnonnal*
Nonnal
Abnonnal
Abnonnal*
Abnonnal*
Nonnal
Abnonnal
Abnonnal
Equivocal
Nonnal
Nonnal
Abnonnal
Nonnal
Equivocal
12
97
76
62
21
19
84
-42
+43
+22
+ 8
-33
- 35
+30
-36
+ 2
*Interpretation in conflict with the statistical interpretation. CAD = coronary artery disease.
18
56
246
ROZANSKI ET AL.
EJECTION FRACTION AND WALL MOTION
is inherently reproducible and allows the concomitant analysis of multiple nonscintigraphic test observations. As with
conventional analysis, our format does not address variations related to subjectivity (52), exercise protocol (38) or
the extent, location and time to onset of wall motion abnormality (53). Unlike conventional analysis, however, these
refinements are readily implemented as the data become
available.
MS. for her statisticallldvice
We gratefully acknowledge Joanne Prause, MS,
and careful review of the manuscript, Patricia Allen, Joye Nunn Hill,
Jiirate Sutor and Barbara Voigt for their technical assistance and Lance
L"forteza for the illustrations.
Laforteza
References
I. Greenberg PS, Ellestad MH, Berge R, et al. Radionuclide angiographic correlation of the R wave, ejection fraction, and volume reIIpright bicycle exercise. Chest 1981;80:459-64.
sponses to lIpright
2. Berger HJ, Reduto LA, Johnstone DE, et al. Global and regional left
ventricular response to bicycle exercise in coronary artery disease.
Assessment by quantitative radionuclide angiography. Am J Med
1979;66: 13-21.
p, Newman GE, et al. Accuracy of diagnosis of
3. Jones RH, McEwan P,
coronary artery disease by radionuclide measurement of left ventricular
function during rest and exercise. Circulation 1981 ;64:586-60 I.
4. Manyari DE, Kostuk WJ. Left and right ventricular function at rest
and during bicycle exercise in the supine and sitting positions in normal
subjects and patients with coronary artery disease. Assessment by
radionuclide ventriculography. Am 1J Cardiol 1983;51:36-42.
5. Maddahi 1,
J, Berman DS, Matsuoka DT, Waxman AD, Forrester lS,
JS,
Swan Hle.
HJC. Right ventricular ejection fraction during exercise in normal subjects and in coronary artery disease patients: assessment by
multiple-gated equilibrium scintigraphy. Circulation 1980;62: 133-40.
6. Borer lS,
JS, Bacharach SL, Green MV, et al. Real-time radionuclide
cineangiography in the noninvasive (evaluation of global and regional
left ventricular function at rest and during exercise in patients with
coronary artery disease. N Engl J Med 1977;296:839-44.
7. Borer lS,
JS, Kent KM, Bacharach SL, et al. Sensitivity, specificity, and
predictive accuracy of radionuclide cineangiography during exercise
in patients with coronary artery disease. Comparison with exercise
electrocardiography. Circulation 1979;60:572-80.
TJ, Thrall lH,
8. Brady n,
JH, Lo K, Pitt B. The importance of adequate exercise
in the detection of coronary heart disease by radionuclide ventriculography. 1J Nucl Med 1980;21: 1125-30.
9. Caldwell JH, Hamilton GW, Sorenson SG, et al. The detection of
coronary artery disease with radionuclide techniques: a comparison of
rest-exercise thallium imaging and ejection fraction response. Circulation 1980;61 :610-9.
V, Ashburn W. Dif10. Pfisterer ME, Battler A, Slutsky R, Froelicher Y,
ferential diagnosis of atypical chest pain syndromes by equilibrium
radionuclide angiography during exercise. Eur 1J Cardio11980; II :425-34.
II. Dehmer Gl,
GJ, Lewis SE, Hills LD, et al. Exercise-induced alterations
in left ventricular volumes and the pressure-volume relationship: a
sensitive indicator of left ventricular dysfunction in patients with coronary artery disease. Circulation 1981;63:
1981 ;63: 1008-18.
EG, Mammen GP, Rivas AH. Postexercise potentiation of
12. DePuey EG.
wall motion to identify myocardial viability (abstr). J Nucl Med 1981;
22:P80.
13. Hecht HS, 10sephson
Josephson MA, Hopkins 1M,
JM, Singh BN. Reproducibility
of equilibrium radionuclide ventriculography in patients with coronary
artery disease: response of left ventricular fraction and regional wall
motion to supine bicycle exercise. Am Heart 1J 1982;104:567-74.
JACC Vol. 5. No.2
lACC
NO.2
February 1985:238-48
14. Manyari DE. Nolewajka AJ, Purves P, et al. Comparative value of
the cold-pressor test and supine bicycle exercise to detect subjects
with coronary artery disease using radionuclide ventriculography. Circulation 1982;65:571-9.
15. Ratib 0, Henze E, Schon H, Schelbert H. Phase analysis of radionuclide ventriculograms for the detection of coronary artery disease.
Am Heart 1J 1982;104:1-12.
16. Sigwart U, Grbic M, Essinger A, et al. Improvement of left ventricular
function after precutaneous transluminal coronary angioplasty. Am 1J
Cardiol 1982;49:651-7.
/982;49:651-7.
17. Tamaki N, Mukai T, Ishii Y, et al. Evaluation of asynchrony by phase
analysis of resting and exercise gated blood pool studies (abstr). 1J
Nuc1
Nucl Med 1982;23:P83.
18. Osbakken MD, Boucher CA, Okada RD, et al. Spectrum of global
ljse of
left ventricular responses to supine exercise. Limitation in the lise
ejection fraction in identifying patients with coronary artery disease.
Am 1J CardioI1983;51:28-35.
Cardiol 1983;51:28-35.
lsosorbide dinitrate-induced
19. Steele PP, Rainwater 1,
J, lensen
Jensen D, et al. Isosorbide
improvement in left ventricular ejection fraction during exercise in
coronary artery disease. Chest 1978;74:526-30.
20. Berger HL
HJ. 10hnstone
Johnstone DE, Sands 1M,
JM, et al. Response of right ventricular ejection to upright bicycle exercise in coronary artery disease.
Circulation 1979;60: 1292-300.
21. Johnson LL, McCarthy DM, Sciacca RR, Cannon PJ. Right ventricular
ejection fraclion
fraction during exercise in patients with coronary artery disease. Circulation 1979;60: 1284-91.
22. Verani
Yerani MS, Delventuri L, Miller BR. Radionuclide ventriculograms
during dynamic exercise and isometric exercise in coronary artery
disease: comparison with exercise thallium-20l
thallium-201 scintigraphy (abstr).
Clin Res 1979;27:21IA.
23. lengo
Jengo lA,
JA, Freeman R, Brizendine M, Mena I. Detection of coronary
artery disease: comparison of exercise stress radionuclide angiocardiography and thallium stress perfusion scanning. Am 1J Cardiol 1980;
45:535-41.
24. 10hnstone
Johnstone DE, Sands MJ,
ML Berger Hl,
HJ, et al. Comparison of exercise
radionuclide angiocardiography and thallium-20 I myocardial perfusion imaging in coronary artery disease. Am 1J Cardiol 1980;45: 1113-9.
lskandrian AS, Hakki A, Kane SA, Segal BL. Quantitative radio25. Iskandrian
nuclide angiography in assessment of hemodynamic changes during
upright exercise: observations in normal subjects, patients with coronary artery disease and patients with aortic regurgitation. Am 1J Cardiol
1981 ;48:230-46.
26. Folland ED, Hamilton GW, Larson SM, et al. The radionuclide ejeclion
tion fraction: a comparison of three radionuclide techniques with contrast angiography. J Nucl Med 1977;18:1159-66.
AL. Hannan T, Brash HM, et al. Comparison of measurement
27. Muir AL,
of ejection fraction by radioisotope techniques and by cineangiography
(abstr). Br Heart 1J 1976;38:875.
28. Folland ED, Hamilton GW. Radionuclide angiography: a comparison
of first pass and gated blood pool methods. Herz 1980;5:121-32.
Fl, Berger HJ, lohnstone
29. Wackers FJ,
Johnstone DE, et al. Multiple gated blood
pool imaging for left ventricular ejection fraction: validation of the
technique and assessment of variability. Am 1J Cardiol 1979;43: 1159-60.
30. Slutsky R, Battler A, Karliner lS,
JS, et al. First-third ejection fraction
at rest compared with exercise radionuclide angiography in assessing
patients with coronary artery disease. Radiology 1980;136:197-201.
V, Conant R. et al. Effects of maximal exercise stress
31. lengo
Jengo lA,
JA, Oren Y,
on left ventricular function in patients with coronary artery disease
using first pass radionuclide angiocardiography. A rapid, noninvasive
technique for determining ejection fraction and segmental wall motion.
Circulation 1979;59:60-5.
32. Kaul S, Boucher CA, Okada RD, Newell JB, Strauss HW, Pohost
GM. Sources of variability in the radionuclide angiographic assessment of ejection fractions: a comparison of first-pass and gated equilibrium techniques. Am 1J Cardiol 1984;53:823-8.
JACC Vol. 5, No.2
February 1985:238-48
33. Rozanski A, Bennan D, Gray R, et al. Preoperative prediction of
reversible myocardial asynergy by postexercise radionuclide ventriculography. N Engl J Med 1982;307:212-6.
34. Christopher TD, Konistaninow G, Jones RH. Bayesian analysis of
radionuclide angiogram data for diagnosis of coronary artery disease.
Circulation 1984;69:65-72.
35. Diamond GA, Forrester JS. Improved interpretation of a continuous
variable in diagnostic testing: probabilistic analysis of scintigraphic
rest and exercise left ventricular ejection fraction for coronary artery
disease detection. Am Heart J 1981;102:189-95.
36. Diamond GA, Hirsch M, Forrester JS, et al. Application of information theory to clinical diagnostic testing. Circulation 1981;63:915-21.
37. Port S, McEwan P, Cobb FR, Jones RH. Influence of resting left
ventricular function on the left ventricular response to exercise in
patients with coronary artery disease. Circulation 1981;63:856-63.
JD, Pollock ML, Schmidt DH. Effect
38. Foster C, Dymond DS, Anholm 10,
of exercise protocol on the left ventricular response to exercise. Am
J Cardiol 1983;51:859-64.
39. Gibbons RJ, Lee KL, Cobb FR, Coleman RE, Jones RH. Ejection
fraction response to exercise in patients with chest pain, coronary
disease, and nonnal resting ventricular function. Circulation 1982;
66:643-8.
D, Morris D, Swan
40. Rozanski A, Diamond GA, Forrester JS, Berman D,
HJe. Comparison of alternative referent standards for cardiac normality. Implications for diagnostic testing. Ann Intern Med 1984; 101:
164-71.
41. Rozanski A, Diamond GA, Bennan DS, Forrester JS, Morris D, Swan
HJe. The declining specificity of exercise radionuclide ventriculography. N Engl J Med 1983;518-22.
42. Osbakken MD, Merril D, Boucher CA, Okada RD, Strauss HW,
Pohost GM. Low end-systolic volume at rest. An explanation for
failure of increase in ejection fraction during exercise in nonnal patients (abstr). J Nucl Med 1980;21:7.
ROZANSKI ET AL.
EJECTION FRACTION AND WALL MOTION
247
53. Kimchi A,
A. Rozanski A,
A. Fletcher C,
C. Maddahi J,
J. Swan HJC,
HJC. Berman
D. The time to onset of exercise wall motion abnormalities aids in
the prediction of the presence and severity of coronary artery disease.
Circulation 1982;66(suppl 11):11-340.
54. Meyer SL. Data Analysis for Scientists and Engineers. New York:
Wiley,
Wiley. 1975.
55. Winkler RL, Hayes WL. Statistics: Probability, Inference and Decision. 2nd ed. Holt, Reinhart, Winston, 1975.
Appendix I
The ejection fraction data in Table I1 (rest and exercise, with
and without disease) were employed to develop a statistical format
for integrated interpretation. First, the mean (1') and standard
deviation (a) for each of the four groups (rest and exercise, with
and without disease) were converted to a beta probability distribution (34-35), from which the relative frequency at any specific
(13) can be determined according to:
level of ejection fraction ({3)
{3
13 = B(p[n,r)
B(pln,r) = ypr-I
'Ypr-I q"-r-I,
qn-r-I,
where p is the measured ejection fraction, q = I1 -
p, nand r
are the parameters of the distribution and y'Y is a constant analogous
to the binomial coefficient, but in terms of the gamma function:
n = pq/cr,
r = pn, and
r(n)/r(r)/nn - r).
y = r(n)/f(r)/nn
The frequency denoted by {3 represents the probability of the specific ejection fraction p being observed, given one of the two
43. Poliner LR, Matlock J, Del Ventura L, Miller RR. Abnonnal ejection
fraction response to exercise in patients with nonnal coronary arteries
and high resting ejection fraction (abstr). Circulation 1981 ;64(suppl
IV):IV-326.
diagnostic states (presence or absence of coronary artery disease).
44. Wassennan AG, Katz RJ, Varma VM, et al. Response to exercise in
patients with high resting ejection fraction: what is abnonnal? (abstr).
Clin Res 1984;31:215A.
for the frequency distribution in the patients with disease, {3 is the
45. Port S, Cobb FR, Coleman E, et al. Effect of age on the response of
the left ventricular ejection fraction to exercise. N Engl J Med 1980;
303:1133-7.
46. Rodeheffer R, Gerstenblith G, Fleg JL, et al. The impact of age on
gated blood pool scan (GBPS) measurements of LV volumes during
IV):IV -243.
exercise. Circulation 1981 ;6 II (suppl IV):IV-243.
47. Bove AA, Bodurian EN. Effect of coronary artery disease on the aging
heart (abstr). J Am Coli Cardiol 1983;1:718.
48. Gibbons RJ, Lee KL, Cqbb F,
F. Jones RH. Ejection fraction response
to exercise in patients with chest pain and nonnal coronary arteriograms. Circulation 1981;64:952-7.
H. Forrester JS, Pollock B, Swan HJC. Com49. Diamond GA, Staniloff H,
puter-assisted diagnosis in the noninvasive evaluation of patients with
disease. J Am Coli Cardiol 1983;1:444-55.
suspected coronary artery disease,
50. Diamond G. CADENZA: Computer-Assisted Diagnosis and Evaluation of Coronary Artery Disease. (Software and Documentation). Seattle: Cardiokinetics,
Cardiokinetics. 1979.
51. Gibbons RJ, Lee KL, Pryor D, et al. The use of radionuclide angiography in the diagnosis of coronary artery disease-a logistic regression analysis. Circulation 1983;68:740-6.
52. Okada RD,
RD. Kirshenbaum HD, Kushner FG, et al. Observer variance
in the qualitative evaluation of left ventricular regional wall motion
and the quantitation of left ventricular ejection fraction using rest and
exercise multigated blood pool imaging. Circulation 1980;61: 128-36.
For the frequency distribution in the patients with disease, {3 is
({3t) of the ejection fraction p. Conversely,
the true positive rate ({3,)
false positive rate (B If ) of p.
The true and false positive rates were first determined for each
of 60 levels of rest ejection fraction (ranging from 0.20 to 0.80
in increments of 0.0 I) and for each of 40 levels of exercise ejection
fraction (ranging from +0.20 to -0.20 relative to the rest value,
also in increments of 0.01). The true and false positive rates for
x 60 or 2,400 rest/exercise combinations were
each of the 40 x
calculated multiplicatively. The variance of each {3 was defined
as:
where a p is the standard deviation of the measured ejection fraction, estimated from the literature review as 0.0534p. The rest and
exercise variances were added without a covariance correction (54)
since the covariance was small. Each pair of true and false positive
rates with their associated variances (for rest ejection fraction,
exercise ejection fraction and the combined resUexercise ejection
fraction response) was then converted into a t statistic (55):
t=
(=
{3,-{3f
f3t-{3f
Vaf3~ + af3~
248
ROZANSKI ET AL.
EJECTION
ElECTION FRACTION AND WALL MOTION
lACC Vol. 5, No.2
February 1985:238--48
Degrees of freedom for t were always > 1000; for all practical
purposes,
pUrPOses, then, t was equivalent to a Z transformation using the
normal distribution. A 50% confidence interval (ze
(ze = 0.6745) was
employed to compare the magnitude of the difference between {3,
f3t
and {3r
f3f given their associated variances.
The following definitions were therefore established relative to
this confidence interval:
Abnormal: {3,
f3t > {3r
f3f and t > Ze'
Equivocal: {3,
f3t < > {3r
f3f and - Ze < t < z" and
f3t < (3r
f3r and t < - Ze'
Normal: {3,
Appendix II
Program Listing
Dat& File
X(2), Y(2),B(2,2),E(2,2),A(2),R(2), V(2),S(4),
K(4),M(4),N,LIRATO
Unit I: Input data set
Unit 2: Output data set
Unit 3: Data set containing numeric constants
DO 1000 1= 1,2
X(I),K(I)
READ( I ,20,END = 9000) X(I),K(l)
K(I) + I
K(I) = K(l)
Y(I) = I - X(I)
CONTINUE
DO 2000 1= 1,2
DO 3000 J= 1,2
READ(3,25,END = 9000) G,RR,N
N=N -RR-I
RR=RR-I
DO 4000 KK= 1,4
READ(3,25,END = 90(0) M(KK)
READ(3,25,END = 9000) S(KK)
CONTINUE
N*LOG(Y (I»)
C = G*EXP(RR
*LOG(X(I» + N*LOG(Y(I»)
G*EXP(RR*LOG(X(I»
D= C*X(I)*ABS(RR/X(I) - N/Y(I)*0.0534
S(K(I)/M(K(I))
EE = S(K(I))/M(K(I))
F=D/C
B(I,1) = C*M(K(I»
B(I,J)
E(I,J) = B(I,1)*SQRT(EE*EE + F*F)
CONTINUE
CONTINUE
DO 5000 J= 1,2
A(J) = B( 1,1)*B(2,1)
A(1)
I ,J)*B(2,J)
,I)1B( I,J)
I ,1)
EE = E( I ,J)lB(
F = E(2,1)/B(2,J)
E(2,J)/B(2,1)
R(J) = EE*EE + F*F + 1.
I. 132*EE*F
V(1) = R(J)*
R(1)* A(J)*
A(1)* A(1)
A(J)
V(J)
CONTINUE
T=
A(I»/SQRT(V(I)
T = (A(2) - A(I
»/SQRT(V(l) + V(2»
Test Result: 0 = Normal I = Abnormal 2 = Equivocal
AA=2
IF(ABS(T).GT. 0.6745) AA = 0
IF (T.GT. 0.6745) AA= 1I
A(2)1A( I)
LIRA
TO = A(2)/A(
LIRATO
A(2))
P = A(2)1(A( I) + A(2»
P**2)*SQRT(R(1) + R(2) + (16./27.»
SD = (P - P**2)*SQRT(R(l)
LIRA TO = Likelihood Ratio
T = T - Statistic
LIRATO
AA = Test Abnormality
P = CAD Probability
SD = Standard Deviation
WRITE(2,30) LIRATO,T,AA,P,SD
FORMAT(2FIO.5)
FORMAT(FI5.7)
FORMAT(F15.7)
FORMAT(5(FI0.6,2X»
FORMAT(5(FI0.6,2X))
CONTINUE
STOP
END
21460115.2
16.3779346
25.7839021
.7450
.0378
.1547
.0184
.0741
.0133
.0262
.0081
2455329.13
13.8190153
22.3031234
.7080
.0273
.1719
.0173
.0870
.0129
.0331
.0082
17738.5429
11.3977115
16.4090290
.9257
.0228
.0509
.0111
.0186
.0069
.0048
.0035
24865.5867
8.70654705
15.2292235
.3912
.0293
.2600
.0200
.2056
.0184
.1432
.0160
REAL
C
C
C
1000
4000
3000
2000
5000
C
C
C
C
20
25
30
9000